x
(
t
)
t
x
t
w
(
a
)
a
s
s
(
t
) =
x
(
a
)
w
(
t
−
a
)
da
s
(
t
) = (
x
∗
w
)(
t
)
w
w
0
x
w
t
x
w
t
s
[
t
] = (
x
∗
w
)(
t
) =
∞
a
=
−∞
x
[
a
]
w
[
t
−
a
]
I
K
s
[
i,
j
] = (
I
∗
K
)[
i,
j
] =
m
n
I
[
m,
n
]
K
[
i
−
m,
j
−
n
]
s
[
i,
j
] = (
I
∗
K
)[
i,
j
] =
m
n
I
[
i
−
m,
j
−
n
]
K
[
m,
n
]
m
n
s
[
i,
j
] = (
I
∗
K
)[
i,
j
] =
m
n
I
[
i
+
m,
j
+
n
]
K
[
m,
n
]
a
b
c
d
e
f
g
h
i
j
k
l
w
x
y
z
aw + bx
+ ey + fz
bw + cx
+ fy + gz
cw + dx
+ gy + hz
ew + fx +
iy + jz
fw + gx +
jy + kz
gw + hx
+ ky + lz
Input
Kernel
Output
m
n
m
×
n
O
(
m
×
n
)
k
k
×
n
O
(
k
×
n
)
k
m
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
X
3
3
X
3
X
3
O
(
k
×
n
)
k
k
m
m
n
k
m
×
n
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
S
3
S
3
3
S
3
S
3
x
1
x
2
x
3
h
2
h
1
h
3
x
4
h
4
x
5
h
5
g
2
g
1
g
3
g
4
g
5
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
x
1
x
2
x
3
s
2
s
1
s
3
x
4
s
4
x
5
s
5
f
(
x
)
g
f
(
g
(
x
)) =
g
(
f
(
x
))
g
g
g
(
x
)
i
g
(
x
)[
i
]
=
x
[
i
−
1]
x
x
x
319
×
280
×
3 =
267
,
960
320
×
280
×
319
×
280
2
×
319
×
280
=
178
,
640
Con
v
olutional La
y
er
Input to la
y
er
Con
v
olution stage:
A
ffi
ne transform
Detector stage:
Nonlinearit
y
e.g., rectified linear
P
o
oling stage
Next la
y
er
Input to la
y
ers
Con
v
olution la
y
er:
A
ffi
ne transform
Detector la
y
er:
Nonlinearit
y
e.g., rectified linear
P
o
oling la
y
er
Next la
y
er
Complex la
y
er terminology
Simple la
y
er terminology
k
k
0.1
1.
0.2
1.
1.
1.
0.1
0.2
...
...
...
...
0.3
0.1
1.
1.
0.3
1.
0.2
1.
...
...
...
...
DETECTOR ST
A
GE
POOLING ST
A
GE
POOLING ST
A
GE
DETECTOR ST
A
GE
0.1
1.
0.2
1.
0.2
0.1
0.1
0.0
0.1
K
i,j,k,l
i
j
k
l
V
i,j,k
i
j
k
Z
i,j,k
=
l,m,n
V
l,j
+
m,k
+
n
K
i,l,m,n
l
m
n
s
c
Z
i,j,k
=
c
(
,
,
s
)
i,j,k
=
l,m,n
[
V
l,j
×
s
+
m,k
×
s
+
n
K
i,l,m,n
]
.
s
m
×
m
k
×
k
m
−
k
+
1
×
m
−
k
+
1
1
×
1
k
m
+
k
−
1
×
m
+
k
−
1
...
...
...
...
...
...
...
...
...
i
j
k
l
m
n
Z
i,j,k
=
l,m,n
[
V
l,j
+
m,k
+
n
w
i,j,k,l
,m,n
]
.
i
l
m
n
m
n
k
t
t
Z
i,j,k
=
l,m,n
V
l,j
+
m,k
+
n
K
i,l,m,n,j
%
t,k
%
t
s
c
(
,
,
s
)
J
(
,
)
c
J
G
i,j,k
=
∂
∂
Z
i,j,k
J
(
,
)
.
g
(
,
,
s
)
i,j,k,l
=
∂
∂
K
i,j,k,l
J
(
,
) =
m,n
G
i,m,n
V
j,m
×
s
+
k,n
×
s
+
l
.
h
(
,
,
s
)
i,j,k
=
∂
∂
V
i,j,k
J
(
,
) =
l,m
|
s
×
l
+
m
=
j
n,p
|
s
×
n
+
p
=
k
q
K
q
,i,m,p
G
i,l,n
.
h
=
h
(
,
,
s
)
.
g
(
,
,
s
)
c
(
,
,
s
)
g
c
h
k
×
k
i,j,
:
=
(
i,
j
)
i,j,
:
2
×
2
d
d
d
k
w
O
(
w
d
)
O
(
w
×
d
)
k
•
•
•
•
•
I
(
x,
y
)
x
X
y
Y
w
(
x,
y
)
s
(
I
) =
x
∈
X
y
∈
Y
w
(
x,
y
)
I
(
x,
y
)
.
w
(
x,
y
)
w
(
x,
y
;
α,
β
x
,
β
y
,
f
,
φ,
x
0
,
y
0
,
τ
) =
α
exp
−
β
x
x
2
−
β
y
y
2
cos(
f
x
+
φ
)
,
x
= (
x
−
x
0
)
cos(
τ
)
+
(
y
−
y
0
)
sin(
τ
)
y
=
−
(
x
−
y
0
)
sin(
τ
)
+
(
y
−
y
0
)
cos(
τ
)
.
α
β
x
β
y
f
φ
x
0
y
0
τ
x
0
y
0
τ
x
y
x
y
x
0
y
0
τ
x
y
w
x
α
exp
−
β
x
x
2
−
β
y
y
2
x
y
α
β
x
β
y
x
0
y
0
τ
x
0
y
0
τ
x
0
y
0
τ
beta
x
β
y
β
x
β
y
β
×
f
φ
f
φ
φ
f
×
cos(
f
x
+
φ
)
x
f
φ
L
2
c
(
I
)
=
s
0
(
I
)
2
+
s
1
(
I
)
2
s
1
s
0
φ
φ
s
1
s
0
s
0
s
1
I
(
x,
y
)
exp(
−
β
x
x
2
−
β
y
y
2
)
f
τ
(
x
0
,
y
0
)
τ